SOLUTION: Hi! My question: find the domain for f(x) = 6th root of 1-4x^2. There is nothing this complex in my entire book!! Where do I start? Do I make a chart and start plugging numbers?

Algebra ->  Rational-functions -> SOLUTION: Hi! My question: find the domain for f(x) = 6th root of 1-4x^2. There is nothing this complex in my entire book!! Where do I start? Do I make a chart and start plugging numbers?      Log On


   

Question 515130: Hi! My question: find the domain for f(x) = 6th root of 1-4x^2. There is nothing this complex in my entire book!! Where do I start? Do I make a chart and start plugging numbers? I was praying for an odd root!! ha-ha Can you please tell me step by step what to do?
You are all life savers!
Thanks,
Tracy
Found 2 solutions by Gogonati, josmiceli:
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Since the 6th root is an even number the radical must be greater or equal to zero
1-4x^2≥0 Solving this inequality we get the domain of f(x) in interval notation:(-1/2, 1/2)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can take a shot at it
+%28+1+-+4x%5E2+%29%5E%281%2F6%29+
+%28+1+-+%282x%29%5E2%29%5E%281%2F6%29+
I'll make the substitution +z+=+2x+
+%28+1+-+z%5E2%29%5E%281%2F6%29+
+%28+1+%2B+z+%29%5E%281%2F6%29+%2A+%28+1+-+z+%29%5E%281%2F6%29+
If z is greater than +1+,
or less than -1 then one
of these 2 factors is negative.
I can rewrite as:
%28+%28+1+%2B+z+%29%5E%281%2F2%29+%2A+%28+1+-+z+%29%5E%281%2F2%29%29%5E%281%2F3%29+
So, any +z+ greater than 1 or less than -1
gives me an imaginary factor. If
+z+%3C+=+1+ or +z+%3E+=+-1+, the expression is real.
Since +z+=+2x+
+-1+%3C=+2x+%3C=+1+
+-1%2F2+%3C=+x+%3C=+1%2F2+ answer
hope I got it